On the ignition of pulverized anthracite

On the Ignition of Pulverized Anthracite J. 0. Central

Electricity

CUTRESS, T. J. PEIRCE and A. C. N. TUCKER

Generating

Board,

Research and Development Near Bris to1 (Received

July

Laboratories,

Portishead,

1964)

Consideration has been given to the mechanisms by which pulverized anthracite ignites ‘in a power station furnace. An equation has been formulated for calculating the ignition delay of a single particle, using the heat transfer process considered to be predomznant from the results of experimental measurements and observations of the pre-ignition zone of an anthracite-fired furnace. The main conclusion from the analysis is that particles in the mixing zone of the jet are temperature, the first to reach ignition mainly because entrainment of hot combustion products around the jet periphery accelerates the rate of heat transfer to the particles. The ignition of particles within the central core of the jet (where gas temperatures are low and the effect of radiation from the refractory and the tail of the flame is diminished) may depend upon the prior ignition of those in the peripheral mixing zone. The calculated time for the ignition delay of a single particle in the mixing zone is much less than the time a particle This is explicable since all the particles do not necessarily takes to travel to the flame front. travel in the mixing zone of the jet, and the ignition of a certain minimum number is necessary the mathematical model could be improved by for a stable flame front. In this respect, including a treatment of the mixing processes. Principles for the design of low volatile coal burners are suggested.

Introduction

DURING an investigation into the improvement of combustion efficiency of pulverized anthracite at Tir John Generating Station (South Western Region C.E.G.B.) consideration has been given to the heat transfer mechanisms by which pulverized anthracite is ignited in the furnace. A theory of ignition is developed to explain the measurements made in the furnace. These ideas are applied to explain ignition in a full-scale boiler and the relevance of this to burner design. Most reference books quote the experimental results of A. DE GREY' and present his results in the form of a graph showing flame speed against ratio of air to coal. The curves for coals of different volatile matter have maxima at certain air to coal ratios, the values of this ratio for maximum flame speed increasing as the volatile content of the coal increases. It has long been realized that the condition under which measurements are made can affect the flame speed and that these results are not necessarily applicable to an industrial furnace. J. CSABA* has carried out work at Sheffield University in which he measured the flame speed in a small pilot furnace. This was deliberately designed to prevent

any mixing back of hot products of combustion and the flame speeds measured were small compared with those met in practice. Both J. CSABA* and J. M. BEBR~ have pointed out the importance of the mixing of recirculated hot gases on ignition. W. NUSSEL? developed a theory of ignition which is discussed below. It is suggested here that the concept of an ignition delay time is more useful than that of a flame speed when dealing with low volatile coal. Description of the Pre-ignition General description

Zone at Tir John

A description of the Tir John furnaces has been given by J. MAYER~ and a brief summary by J. 0. CUTRESS and T. J. PEIRCE~. The combustion chamber is rectangular in cross section (24; ft x 209 ft) and 27 ft deep with a watercooled ash hopper at the base. Primary air and fuel are discharged from ten burners set closely together in a refractory arch at the top of the front wall firing downwards. Each burner mouth is a divergent rectangular nozzle with an exit of 19; in x St in. The flow pattern in the furnace chamber was

J. 0. Cutress, T. J. Peirce and A. C. N. Tucker

290

Vol.

s

of 2 : 1.) The primary air is preheated to a much higher temperature than is usual for pulverized coal. The design air temperature was apparently 295°C but, in practice, a temperature of 370°C is obtained. A bin and feeder system is used, and after the coal and primary air are fully mixed the temperature is 260°C. Furnace

Figwe

1.

Main

features

of furnace

flow pattern

investigated with a scaled-down water model? and Figure 1 illustrates the processes that can be detected. Primary air and coal enter through the burners (A). The primary jet penetrates downwards initially, and subsequently turns towards the furnace outlet (B). The approximate position of the ignition zone is shown at (C). As the jet enters the furnace the surrounding fluid is entrained into the jet from sides (D) and (E). Observation of the moving flow pattern revealed a reversed flow up the front wall at (D). The flow was subsequently entrained into the jet in a series of eddies. The processes occurring in the hot furnace will undoubtedly be more complicated than in the water model but the general description given was shown to be valid by observations on the patterns of ash deposited on the refractory walls of the boiler. Supply of coal and air The primary air to coal mass ratio at the burner is approximately 4 : 1 and the jet velocity calculated as an average over the burner nozzle area is of the order of 50 ft / set, falling to some 20 ft /set before ignition occurs. (A flame speed of 20 ft jsec is not in agreement with the measurements quoted by de Grey which would predict for anthracite a flame speed of about 5 ft jsec at the above air to coal ratio, rising to a maximum of 10 ft /set at an air to fuel ratio

measurements

Measurements of gas temperature, velocity and solid content were made in the pre-ignition zone of the furnace employing water-cooled probes similar to a design used by &I. E. PEPLOW*. A standard probe was used as a carrier for alternative sampling and temperature measuring instruments. The probes could be inserted to various horizontal distances within the furnace through ports constructed on the axis of a burner at distances of 20, 30, 56 and 72in. vertically below the refractory burner arch. The detailed discussion below refers to measurements made with a low load of 140 k lb/ h on the boiler; these measurements are summarized in Figures 2 and 3. The maximum continuous rating of the boiler is 230 k lb/ h but high furnace temperatures limited extensive measurements to the lower load. Some measurements were made at a load of 200 k lb/h and confirm the general pattern with higher gas temperatures. Temperature measurements were made by two means, with a suction pyrometer and a bare thermocouple. A bare thermocouple will not record the correct temperature of the gas, as it will gain or lose heat by radiation to its surroundings. A suction pyrometer has a radiation shield, and will be assumed to measure the temperature of the gas, (In fact the presence of coal particles at a different temperature from the gas will also affect it.) It should be noted that differences between the two measured temperatures indicate the presence of a radiation field, a higher temperature with a bare thermocouple s’rlowing that it is receiving radiation from its surroundings. Primary air and coal enter the furnace at a temperature of 260°C through a burner nozzle 18 in. long. At a distance of 20in. below the burner nozzle outlet the temperature at the centre of the jet is increased to between 500”

December

1964

On the ignition of pulverized anthracite

291

;Port

70 I

A

620 905 910 980 1060 1115 ii00 1210 1135 1140 1125 1290 ,340 ;925~~~000~~070~:107~'i155][1130][1165][1125]~03~[925][965][1080][1260] Port 0

Distance

from

front

wall,

feet

-

Figwe 2. Temperutwes measured in pve-ignition zone at Tir John at 140 k lb/h load. All temperatures. “C. Suction fiyvometrr results shown unbracketed: bare thermocouple values shown bracketed

and 550°C. The jet appears to be well defined for about the first three feet of its length. The temperature at the centre of the jet is not appreciably raised further until it reaches within one foot of the ignition zone. On each side of the jet a temperature gradient is formed due to its mixing with the surrounding fluid at a temperature of approximately 1200°C on the furnace side and less than 900°C on the wall side. At i’2in. below the burner the temperature of the gas has risen to over 1 lOO”C, even at the centre of the jet, indicating a general region of ignition. Thereafter, the flame rapidly acquires a temperature of approximately 1500°C. The differences between the bare and shielded thermocouples (Figure 2) indicate a strong radiation field from the front wall and arch to

the outside of the coal jet. However, the two temperatures are almost identical in the central core, showing that the radiation has not penetrated through the coal mixture. Velocity measurements were extremely difficult to interpret because of the high degree of turbulence. The fluctuations in readings increased as the distance below the burner increased and there was extremely agitated air flow between the jet and the front wall. The mean velocity was about 20 ft / set across the jet and did not appear to change greatly with increasing distance from the burner (Figure 3). The quantities of solids samples could not be relied upon because of these turbulent conditions, The results show that coal is present across the width of the jet at the first three ports.

Vol. 8

J. 0. Cutress, T. J. Peirce and A. C. N. Tucker

292

reduction in preheat temperature from 250” to 210°C did not affect ignition stability, or the distance between flame front and burner nozzle.

B

Buincr

2

3

4

I ---Port

B(30in)

a -Port

C(56inl

5

6

7 feet

When the Tir John furnaces were first commissioned, one feature of the original burners was the provision of additional air concentric to the primary air jet. Operating experience showed that stability was difficult to maintain. In the light of current results, showing that part of the fuel stream mixes with the hot entrained combustion gases, it may be considered that ignition was poor with the original burner arrangement because the mixing process was delayed.

Theoretical

Examination

of Problems

General considerations

L

0

1

2

3

4

3

‘1 \ 4!a

a

>

2oo

1

2

Distance from front Figure

5

5

6 feet

6

1 7

7/

wall, feet

Temperature, velocity and fixed carbon 3. surveys at Tir John at 140 k lb/h load

The carbon content of the samples collected shows little difference from that of the pulverized coal in the centre of the jet, but there is a reduction of carbon at the edges of the jet, particularly at the two upper ports (Figuw 3). There are two possible explanations of this. One is that the coal was burning. The other is that the ash content of the sample is increased due to the presence of ash and unburnt carbon contained in the recirculated gases mixed into the jet. The effect of preheat temperature on the ignition delay has been studied in a series of furnace trials. Visual observation showed that a

One useful way of studying ignition behaviour is to consider the heat transfer processes by which single particles reach ignition temperature. The possible processes may be tabulated from an overall study of the pre-ignition zone and its environment, and the magnitude of the processes may be established from the experimental measurements. It was evident that, using a heat balance on a single particle, no single delay time could be postulated for ignition as a whole since the results have shown that, for the particular system studied, the jet consists of an outer mixing zone surrounding a cooler potential core. In the first region, heat will reach a particle by radiation from the surrounding flame and refractory, by radiation and conduction from the flame front, and also by conduction from the entrained high temperature fluid. In the second region, the measurements show that the radiation has a negligible effect because of screening by particles in the jet periphery. The measured low temperatures on the jet axis indicate that the particles lose rather than gain heat by conduction to the fluid. Across the temperature gradients exist, mixing zones although the temperature is relatively constant in the potential core. Experiment shows that turbulent eddies occur in the jet, and that the position of the flame front fluctuates.

December

On the ignition

1964

of pulverized

List of Symbols radiation cal cm-’ set-1 degrees-4, constant CP cal g- 1 ‘C-l, specific heat of coal cal g- 1 ‘C-l, specific heat of air particle radiation factor correcting Q, for effective surface area available for radiation absorption f.! particle radiation factor correcting the radiation Q2 for both attenuation factor and effective surface area available for radiation absorption K, cal cm-l set-1 ‘C-l, thermal conductivity of air K photo-extinction coefficient L cm, distance of flame front from burner nozzle n number of particles per unit volume of suspension P = 3K, / rzppcP constants used in dertvaS = 3Kp,v /4rp, tion of equations cal -. crnd2 set-l. flame front radiation (recal crnm2 set- '1, external radiation fractory and radiation from tail of flame) Pa (g cm-“) air density PP (g cm-“) particle density cm, particle radius R’ volume of air per unit mass of fuel t set, time set, ignition delay li V cm see-‘, fluid velocity W cm set-l, velocity of flame propagation particle emissivity particle temperature 6/G di “C ignition temperature of fuel 6, “C original (preheat) temperature of fuel 6f “C flame front temperature 6, “C gas temperature 6,,. “C refractory wall temperature P air to fuel ratio factor for the fraction of rp Nusselt’s radiation received by the coal o-

“r:

&:

Previous theoretical work W. NUSSELT~ first treated the ignition of pulverized coal by formulating a heat balance on a single particle. He did not recognise, however, the fact that a jet necessarily entrained surrounding fluid and that, as a result, the calculated ignition delay would depend upon the local fluid temperature. Nusselt considered the effect of conduction

293

anthracite

from the flame front on the particle temperature at successive distances behind the front, and established an equation giving the speed of heat conduction back from the flame front through rows of un-ignited particles. The equation may be written w= 2(4~~,R/3)-~/~

*1

. f ;fi

0

. . . . PI

where the symbols are as listed above, and the function f is an inverse error function defined by Nusselt. The flame speed is thus a function of a number of properties of the coal (radius, density, ignition temperature, flame temperature) and of the thermal diffusivity and quantity of air associated with it, but is not a function of the burner geometry or furnace characteristics. The theory assumes that as soon as a particle reaches the ignition temperature (0<) it instantaneously assumes a flame temperature, (#0,), and this row of particles commences to heat the oncoming row. it is also assumed that the particles immediately reach the temperature of the air with which they are in contact so that the theory will overestimate the rate of flame propagation. The flame speeds predicted for pulverized fuel by this formula are much too low, of the order of 0.1 ft /set, for this mechanism to account for the ignition observed at velocities of 20 ft/ set at Tir John. Nusselt also considered a particle heated by radiation from surrounding refractory but losing heat to the surrounding air. This gives an expression for the ignition delay ti before a coal particle reaches the ignition temperature which is a special case of the equations developed and discussed in the next section. Nusselt’s expression may be written

Bi=ls”+qy$ n .[I-exp(-s)]...[Z] This equation predicts a critical size of particle below which finer particles will take longer to ignite because they lose heat more rapidly by conduction to the surrounding air than the coarser particles. This is not in accordance with experience, since finer grinding has never been found to worsen ignition stability. It will be shown below that in the mixing zone of a jet, this anomaly is removed.

J. 0. Cutress,

294

T. J. Peirce and 4. C. N. Tucker

Nusselt only considered the heating processes leading to equations 1 and 2 as occurring independently. It can be shown that the effect of conduction from the flame front can be neglected at Tir John. Equation 1 can be re-interpreted as meaning that if un-ignited fuel is flowing towards a flame front with a velocity W, then the fuel must be at a certain temperature (0, in equation 1) for further heating by conduction only to cause ignition. A simple calculation based on current experimental results shows that although conduction raises the temperature of the next row of particles about to ignite at the flame front, it has a negligible effect on the temperature of the row beyond that. Since conduction is only appreciable over this small distance, all the other heating processes would need to raise the temperature of the coal particles to the temperature 8, up to a distance of about one row away from the flame Velocity,

ftlsec

Present

theoretical

Vol.

S

treatment

The treatment below is concerned with the behaviour of a single particle surrounded by a fluid of constant temperature. The rate of temperature rise of a single particle will depend on heat received by radiation and the heat loss to (or gained from) the surrounding fluid. Consider a spherical particle of radius Y moving with a steady velocity v towards a flame front. The time t is measured from the moment the particle leaves the burner mouth. The rate of absorption of heat by the particle is equal to the sum of three terms : (4 Heat gain by radiation from the flame front; an exponential fall off with distance from the flame front is assumed because of screening effects of other particles. (b) Heat gain by radiation from an external field; it is assumed that the energy loss by re-radiation from the particle is small in comparison with the radiation absorbed. (4 Heat loss, or gain, by conduction to surrounding fluid, assumed at constant temperature; for simplicity, it is assumed that the fluid temperature around a particle is constant throughout its trajectory in the pre-ignition zone. This term is negative or positive depending on whether the surrounding gas is hotter or colder than the particle. The heat balance is then _

zxr?f ,Q,

e-Krrzn

(L-d)

+ w2f2Qa - 47cK,v ($0,- 0,) Velocity,

mlsec

Figure 4. Effect of conduction from jiame front. Temperature to which particles must be heated for ignition at 870°C

front. It is seen from Figure 4, calculated from equation 1, that for the flow velocities of 20 ft /set measured at Tir John this temperature is very close to the ignition temperature itself. It follows also that conduction from any external source also has a negligible effect on the ignition delay, and will not be considered further. The only conduction mechanism that needs to be considered is that to or from the fluid surrounding a particle.

where the symbols have the stated meanings. This equation can be integrated, noting that 10p=O, at t =O. The ignition delay, tj, is then defined by putting 10P=lOi (the ignition temperature) at t= t,=L/v, giving

wf ,Q1 (1 - e-u’+S)ti) O-I - 0 0e-pLi = (4& + 4r3p,c,S/3) +

(1 -e-l”)) (8,.+~@)

. . . [3]

This equation has been solved graphically. One special case of the equation is obtained for Q, =0 and 8,= 00, giving the equation for heating by a constant radiation source obtained by NusselP.

December

On the ignition

1964

Calculated

Ignition

of pulverized

Delays

Equation 3, assuming a constant fluid temperature, can be applied to gain some understanding of the ignition processes in the Tir John furnace. Two extreme cases are considered. (1) The case of a particle travelling in the centre of the jetthe potential core. Here it is known from measurements that the temperature is relatively low and constant, and that external radiation does not penetrate, so Q, is zero. (2) For comparison, the case of a particle travelling in the mixing zone surrounded by fluid at the average temperature of this zone, which is the average of the temperatures of the potential core and the surrounding hot gases. It can be envisaged that this case gives some measure of the rate of heating of particles travelling in a turbulent manner in this zone. Solutions of equation 3 have been found graphically using quantitative values that are discussed in the Appendix and summarized in Tables 2 and 3. The constant external radiation field Q, is that from the refractory wall and tail of the U-shaped flame, attenuated by a constant factor f, due to absorption in the neighbouring particle-laden fluid. It is assumed that the ignition temperature of anthracite is 87O”C, a value reported from measurements of a cloud of 44~ diameter particle9. The results have also been calculated for a lower ignition temperature of 67O”C, which is the comparable ignition temperature for bituminous coal. This gives some idea of how bituminous coal would behave, although it assumes that similar temperatures would be maintained. Typical results are given in Table 1 showing the ignition delays at two different loads for particles of 76~ diameter (200 mesh). The two cases of the potential core and the average temperature of the mixing zone are given. In addition the case of the mixing zone if there were no external radiation (f2 =O) is also given. An infinite time is sometimes predicted in the potential core and this means that a particle would never reach ignition temperature by the heating processes considered. The results clearly indicate that ignition would start in the mixing zone. In practice once some particles are ignited they will transfer heat to the other un-ignited

anthracite

Table

1.

295

Calculated ignition delay particles (Milliseconds) Character

Load

COZ

for

Mixing

mesh

zone

140 k lb/h

Assumed

gas tem~.

Assumed

radiation

0,“C

500 0

Anthracite

(ignition

870°C)

00

26

670°C)

n

10

(ignition

0

2.7 Ignition

Bituminous

750

750

factor,

cf.2

Load

200

delay

kzsec) 40 12

1

200 k lb/h

Assumed

gas tem~.

Ammed

radiation

0,-C

700

1 050

0

et.,

2.7 Ignition

Anthrncife Bituminous

(ignition (ignition

1 050

factor,

870°C) 670°C)

0 delay

(mm)

lx

9

10

14

5

6

particles. The final column of Table 1 indicates that the external radiation field Qz is not as important as the heating by the fluid in the mixing zone, since if Q,=O, the ignition delay is increased much less than if the particles travel in the core. The prediction that the external radiation field is of more importance for igniting anthracite than coals of lower ignition temperatures is in accord with experience. The actual ignition delay observed at Tir John is about 200 msec at a load of 140 k lb/h, and less at higher loads, which is an order of magnitude greater than the calculated delay even for 200mesh particles. A range of ignition delays could be calculated, by assuming a number of constant temperature paths. The delay time calculated above is that from the time a particle enters the mixing zone to the instant it ignites. In practice, the particles will gradually be entrained into this zone, and there will be a minimum number necessary to form a flame front, where the greatly enhanced heat transfer ignites the remainder of the cloud. The present calculations show that the mixing zone controls ignition and a better understanding of the mixing processes is needed for a quantitative theory. The effect of particle size on the ignition delay is shown by equation 3 to depend upon whether or not the particle temperature exceeds fluid temperature. If this happens, the particles lose heat to the surrounding fluid, the finer particles losing heat more rapidly than the coarse. Combined with other heat transfer mechanisms this could result in the finer particles having a longer

J. 0. Cutress, T. J. Peirce and A. C. N. Tucker

2%

ignition delay than the coarse. However, if the fluid temperature is greater than the ignition temperature, as is assumed to occur over part of the mixing zone, a cloud containing finer particles will have a shorter ignition delay, which is in accord with experience that finer grinding gives better ignition. The effect of pre-heat temperature is shown in Figwe 5, and confirms that much larger

‘C E

101

100

I

/

200 300 Pre-heat temperature,@ OC

J

400

Figure 5. Variation of ignition delay with pre-heat 3 temtwroture for mix&p Wolfeat 200 k lb/h. Equation witliout PN& front r&Cation. Anthracite, Bi=87O”C (76~ diameter particles)

variation in pre-heat temperature than the 40°C range studied experimentally would be required to have an appreciable effect on ignition delay. Discussion

The calculations indicate the importance of entrainment of recirculated gases on the heating of the coal particles in the pre-ignition zone. It should be possible to design a burner in which a sufficiently large number of particles are entrained into such a zone close to the burner, thus giving a flame front nearer the burner mouth. It is advantageous to encourage the recirculation of combustion products back to the burner and to provide some refractory to radiate heat. It is claimed that anthracite burners have been designed in the U.S.S.R. on these principles’“. Before the present investigation it was not known which aerodynamic effects were important for stabilizing ignition. Besides the recirculation of hot gases it had been suggested that eddies induced in the jet (e.g. by the mixing of the secondary air) by fluids of a lower temperature than the jet could stabilize a flame front in their vicinity. (Such mechanisms are

Vol.

8

common experience in the ignition of liquid fuels.) Such effects may well occur on the periphery of the jet and there is some evidence that the impingement of secondary air at Tir John aids ignition, presumably by forming vortices which hold the particles in the jet, allowing them time to reach ignition temperature. The results would seem to indicate, however, that there is sufficient time for heating to ignition temperature to occur in the mixing zone without such aids. The importance of the entrainment of recirculated combustion products has been emphasized by recent results on the horizontal furnace at I Jmuiden”. When additional air was applied, concentric to the burner, stable ignition was only obtained by accident if buoyancy effects caused a separation of the two streams. This is similar to the early operating experiences at Tir John with concentric jets. Conclusion

The mathematical model used for calculating ignition delay is, like previous theories, onedimensional. It is sufficient to show that ignition of anthracite is controlled by the fluid-mixing processes around the jet, and that therefore the processes are not one-dimensional. Further improvement of the theory of ignition needs to include a quantitative treatment of these processes. The flame speed is defined as the rate at which a flame is propagated through un-ignited fuel. To quote a flame speed implies that a stationary flame front is formed when the fluid velocity normal to it is equal to the flame speed. It is not possible with the complex heat transfer processes summarized by equation 3 to derive a speed of propagation (as it would be if conduction were the controlling process leading to equation 1). Indeed, it proves that a stationary flame front is not necessarily formed where the fluid velocity has reached a certain value. Thus the concept of a flame speed is not applicable to pulverized coal. It can be replaced by calculated ignition delay times. The authors would like to thank Mr A. Cadman, Station Su$erintendent, Tir ,John Station, C.E.G.B. South Western Generating

December

attenuation

Region, for allowing the measurements to be taken on his plant. This paper is published by permission of Mr A. C. Thirtle, Regional Director, C.E.G.B. South Western Region.

to

References A. Rev.

Numerical values

f2 corrects

the external

Table 2.

Values

Used

of parameters

Numerical

radiation values

fl, f2 and K

QL both

effective

surface

for

of variables used in analvsis: 140 k lb/k boiler load. core

area

exposed

If the flame front is considered as a plane, and that diffuse or scattered radiation is small in comparison with the ‘direct’ radiation, a value of fl =2 may be assumed, i.e. the particles are only receiving heat over one half their surface area. The photo-extinction coefficient, K, is considered to depend upon the ratio of particle radius to wavelength of the radiation and the refractive index of the particle relative to that of the mediumll. In the current treatment, it has been assumed that the particles are opaque, and that their radius is much larger than the wavelength of the incident radiation. Accordingly K = 1. An assumption that K = 1.W showed that the differences in calculated particle temperatures were less than 4°C.

APPENDIX Numerical

and

radiation.

Its value depends upon the location of the particle within the cloud. fz would approach a maximum value of 4 for particles very close to the refractory wall, since the whole surface (47cr’) would receive radiation. Both calculations and measurements showed that f2 was much lower in the centre of the jet. Furnace observations showed that few un-ignited particles passed close to the front refractory wall. Accordingly the computations were carried out for f2=Oand3.

M&tall. 1922, 19,645 2 CSABA, J. Private communication, 1963 3 BEBR, J. M. ‘Combustion of pulverized coal’. Paper Institute to Conference on Flames and Industry. of Fuel: London, 1962 4 NUSSELT, 137’. ‘Process of combustion in pulverized coal firing’. Z. Ver. dtsck. Ing. 1924, 68, 124 6 MAYER, J. J. Inst. Fuel, 1938, 12, 305 6 CUTRESS, J. 0. and PEIRCE, T. J. To be published 7 BLANCHARD,M. H. J. Inst. Fuel. To be published 8 PIX~LOW, M. E. Paper No. 7 to Second Conference on Pulverized Fuel. Institute of Fuel: London, 1957 n Babcock and \Vilcox Ltd. Steam, Its Generation and Use, New York, 1955 10 KISELGOF, M. and SHEINEK, G. A. ‘Rational methods of fuel consumption with small discharge of volatiles’. Energetika, 1955, 3, No. 11, 1 I’ LEWIS, P. C. and LOTHIAN, G. F. Paper C.2, ‘Physics of particle size analysis’. Brit. J. appl. Pkys. 1954, Supplement No. 3, S71 12 HERDAN, G. Small Particle Statistics, 2nd ed., p 195. Butterworths: London, 1960

1 DEGREY,

297

On the ignition of pulverized anthracite

1964

of jet

Potential

,

Variable Jet velocity Ignition temperature Flame front radiation Air 1fuel mass ratio Thermal conductivity of aiv Photo-extinction coefficient Particle specific heat Particle radius External radiation field Particle radiation factor Particle radiation factor Fluid temperature Particle density Particle emissivity

Symbol

._

-

Magnitude

Units

610 870 [670] 13.4 4 124x 10-G 1.0 0,223 33x 10-k 3.57 1.8 0 and 2.7 500 1.58 0.9

cm jsec “C call cm2 SPC cal cm-1 set-1 deg-1 Cal/g “C cm call cm2 .wc -

F g /cm,?

-

For mixiw zone calculations. Hm=750”C. The thermal conductivity of the medium (air) was changed to K,=158XlO-‘. The flame front and external radiation were assumed to be from black body sources at temperatures of 1 500°C and 1 OOO’C.in accord with exuerimental measurements.

Cross

Vol.

J. 0. Cutress, T. J. Peirce and A. C. N. Tucker

298

sectional

a7ea

of

fiarticles

The cross sectional area should strictly be based on the size distribution of all the particles present. This has not been done in the present calculations, but a general expression can be given. The size distribution of the particles is a good approximation to a logarithmic distribution (measured on a Coulter counter). It can Table

3.

Numerical

values

of variables

be shown12 that the projected specific area of the particles per unit weight (S,) is given by log 4s, = log (.ss / a”&) - log x;, + 1.15 log2 CT0 . . . . [4] where x’, is the geometric mean of the logarithmic distribution by weight, q(Tgits geometric standard deviation, ,E~the surface shape factor, and a, the volume shape factor.

used in analysis:

core of jet

200 k lb/h

boiler load.

Potential

Variable

Symbol

Jet velocity Ignition temperature Flame front radiation Air /fuel mass ratio Thermal conductivity of air Photo-extinction coeficient Particle specific heat Particle radius External radiation field Particle radiation factor Particle radiation factor Fluid temperature Particle density For mixing

zone

calculations,

.-

Magnitude

Units

1 220 870 [670] 13.4 4 152x 10-e 1.0 0.228 38X 10-4

cm jsec

3.57

1.8 0 and 2.7 700 1.58 B,=l

050°C.

The

thermal

8

conductivity

of the medium

(air)

“C cali cm2 set cccl cm-1 set-1 deg-1 Cal/g “C cm cal / cm? set -

was K,=195X10-6.